On Wed, 11 Oct 2017 at 18:16 Alex Smith <ais...@alumni.bham.ac.uk> wrote:
> Gratuitous: mathematically, "A is equivalent to B" means the same thing > as "B is equivalent to A", but I'm not at all convinced that the > mathematical wording was meant in this case. The intended meaning to me > seems closer to "A should be treated as though it were B instead", > which does not necessarily imply that a B should be treated as though > it were an A. The absurdity concluded from the mathematical meaning > here might be a hint that it isn't the meaning that should be in use. > > I'm not currently sure whether this changes the conclusion, but it > needs to be addressed in the reasoning. > > -- > ais523 > The mathematical meaning does not necessarily lead to an absurd conclusion, as I showed. Regardless, if we use a one-way definition, I think the conclusion is the same, because we can't reason backward to conclude that grok's vote indirectly endorsing G. counts as an endorsing vote. It might be possible if 2127 said that an endorsing vote has a value equal to the endorsed player's vote, but it specifically says equal to the endorsed player's valid vote. Thus Aris's vote must be resolved first in order to determine grok's vote, and grok's vote is never interpreted as endorsing G.
